Finite Group Databasebeta

← #14764882

Subgroups — #14764882

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622739C211yesmaximal, characteristic, complemented
3C4×#66990C211yesmaximal, characteristic
4#13069412C211yesmaximal, characteristic, complemented
5#13069408C211yesmaximal, characteristic, complemented
6#13069230C211yesmaximal, characteristic, complemented
7#13069223C211yesmaximal, characteristic, complemented
8#13069220C211yesmaximal, characteristic, complemented
9#13069220C211yesmaximal, characteristic, complemented
10#13068911C211yesmaximal, characteristic, complemented
11#13068911C211yesmaximal, characteristic, complemented
12#13068799C211yesmaximal, characteristic, complemented
13#13068525C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66990C411yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic, complemented
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic, complemented
26C2×C11×C22⋊C8C2211yescharacteristic, complemented
27#10622833C411yescharacteristic
28C4×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
31#10622739—24no—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×#66879C2211yescharacteristic, complemented
41C2×Dic11⋊C8C2211yescharacteristic, complemented
42C2×Dic11⋊C8C2211yescharacteristic, complemented
43C2×C8×Dic11C2211yescharacteristic, complemented
44#10622625—24no—
45#10622602C411yescharacteristic
46#10622602C411yescharacteristic
47#10622569C411yescharacteristic
48#10622569C411yescharacteristic
49#10622568C411yescharacteristic
50#10622559C411yescharacteristic
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4×C11⋊C8C2211yescharacteristic, complemented
55C11×#336C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622188C2211yescharacteristic, complemented
61C24×D11C2×C411yescharacteristic
62C22×D4×C11C2×C411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C23×Dic11C2×C411yescharacteristic
68C22×C4×D11—22no—
69C22×C4×D11—22no—
70C22×C4×D11—41no—
71C22×C4×D11—41no—
72C22×C4×D11—41no—
73C22×C4×D11—41no—
74C22×C4×D11C2×C411yescharacteristic
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C2×C11×M16—22no—
79C2×C11×M16—41no—
80C2×C11×M16—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C2×C11×C4⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11C2×C411yescharacteristic
92C2×C22⋊Dic11C2×C411yescharacteristic
93C2×C22⋊Dic11C2×C411yescharacteristic
94C2×C22⋊Dic11C2×C411yescharacteristic
95#66990—24no—
96C4×C22⋊D11—41no—
97C4×C22⋊D11—41no—
98C4×C22⋊D11—41no—
99C4×C22⋊D11—41no—
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×(C2×D11)⋊C4C2×C411yescharacteristic
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×(C2×D11)⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C2×#4318—22no—
111C2×#4318—41no—
112C2×#4318—41no—
113C2×#4318—41no—
114C2×#4318—41no—
115C2×#4318D414yescomplemented
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C11×C22⋊C8—22no—
121C11×C22⋊C8—41no—
122C11×C22⋊C8—41no—
123C11⋊#95C2×C411yescharacteristic
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—41no—
136(C2×D11)⋊C8—41no—
137(C2×D11)⋊C8—41no—
138(C2×D11)⋊C8—41no—
139#66879—41no—
140Dic11⋊C8—41no—
141Dic11⋊C8—41no—
142C8×Dic11—41no—
143C4⋊(C11⋊C8)—22no—
144C4×C11⋊C8—22no—
145#22038—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—41no—
152C23×D11—41no—
153C23×D11—41no—
154C23×D11—41no—
155C23×D11C22×C411yescharacteristic
156C23×D11C22×C411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—41no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11#4112yes—
176C22×C4×C11C2411yescharacteristic
177C2×C22⋊D11—22no—
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—41no—
181C2×C22⋊D11—41no—
182C2×C22⋊D11—41no—
183C22×Dic11—22no—
184C22×Dic11—41no—
185C22×Dic11—41no—
186C22×Dic11C22×C411yescharacteristic
187C22×Dic11C22×C411yescharacteristic
188C22×Dic11C22×C411yescharacteristic
189C22×Dic11C22×C411yescharacteristic
190C22×Dic11C22×C411yescharacteristic
191C22×Dic11C22×C411yescharacteristic
192C2×C4×D11—22no—
193C2×C4×D11—22no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—41no—
207C2×C4×D11—41no—
208C2×C4×D11—41no—
209C2×C4×D11—41no—
210C2×C4×D11—44no—
211C2×C4×D11—44no—
212C2×C4×D11—44no—
213C2×C4×D11—44no—
214C11×M16—44no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C11×C4⋊C4—22no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C42×C11—21no—
231C42×C11—21no—
232C22⋊Dic11—22no—
233C22⋊Dic11—41no—
234C22⋊Dic11—41no—
235C22⋊Dic11—41no—
236(C2×D11)⋊C4—22no—
237(C2×D11)⋊C4—22no—
238(C2×D11)⋊C4—41no—
239(C2×D11)⋊C4—41no—
240(C2×D11)⋊C4—41no—
241(C2×D11)⋊C4M1614yescomplemented
242Dic11⋊C4—41no—
243Dic11⋊C4—41no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11—21no—
247C4×Dic11—21no—
248#4318—44no—
249#4318—44no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8C2×D412yes—
261C2×C11⋊C8C2×D412yes—
262C2×#436—111no—
263C2×#407—111no—
264C4×#120—111no—
265#1955—111no—
266#1954—111no—
267#1924—111no—
268#1923—111no—
269#1923—111no—
270#1923—111no—
271#1870—111no—
272#1870—111no—
273#1870D1111yescharacteristic, complemented
274#1851—111no—
275#1779—111no—
276#1753—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11C4×D412yes—
291C23×C11C23×C411yescharacteristic
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11—44no—
308C22×D11—44no—
309C22×D11—44no—
310C22×D11—44no—
311C22×D11C2×M1612yes—
312C22×D11#13112yes—
313D4×C11—44no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11C4×D412yes—
333C2×C4×C11C2×M1612yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C22⋊D11—44no—
341C22⋊D11—44no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—44no—
360C2×Dic11C2×M1612yes—
361C4×D11—44no—
362C4×D11—44no—
363C4×D11—41no—
364C4×D11—41no—
365C4×D11—41no—
366C4×D11—41no—
367C4×D11—41no—
368C4×D11—41no—
369C4×D11—41no—
370C4×D11—41no—
371C8×C11—41no—
372C8×C11—41no—
373C8×C11—41no—
374C8×C11—41no—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C11⋊C8—41no—
378C11⋊C8—41no—
379C24×C4—111no—
380C22×M16—111no—
381C22×M16—111no—
382C22×M16C2×D1111yescharacteristic
383C2×#120—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4C2×D1111yescharacteristic
387#436—224no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8—111no—
390C2×C4⋊C8—111no—
391#407—224no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×C22⋊C8—111no—
398C2×C22⋊C8—111no—
399C2×C22⋊C8—111no—
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×C22⋊C8C2×D1111yescharacteristic
403C2×C22⋊C8C2×D1111yescharacteristic, complemented
404C2×C22⋊C8C2×D1111yescharacteristic, complemented
405C2×#97—111no—
406C2×C4×C8—111no—
407C2×C4×C8—111no—
408#386—111no—
409#386—111no—
410#386—111no—
411#385—111no—
412#385—111no—
413#385—111no—
414#379—111no—
415C4×C22⋊C4—111no—
416C4×C22⋊C4—111no—
417C4×C22⋊C4—111no—
418#336—111no—
419#336—111no—
420#336—111no—
421#336—111no—
422#336C2×D1111yescharacteristic, complemented
423#336C2×D1111yescharacteristic, complemented
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11C2×C4×D411yescharacteristic
439C22×C11#51811yescharacteristic
440C22×C11#51811yescharacteristic
441C22×C11C22×M1611yescharacteristic
442C22×C11C2×#13111yescharacteristic
443C22×C11#56811yescharacteristic
444C22×C11#56811yescharacteristic
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—416no—
452C2×D11—41no—
453C2×D11—41no—
454C2×D11—41no—
455C2×D11—41no—
456C2×D11—41no—
457C2×D11—41no—
458C2×D11—41no—
459C2×D11—41no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—41no—
463C4×C11—41no—
464C4×C11#53411yescharacteristic
465C4×C11#53511yescharacteristic
466C4×C11#53811yescharacteristic
467C4×C11#53811yescharacteristic
468Dic11—22no—
469Dic11—41no—
470Dic11—41no—
471Dic11—41no—
472Dic11—41no—
473Dic11—41no—
474C25—111no—
475C22×D4—111no—
476C22×D4—111no—
477C22×D4C4×D1111yescharacteristic
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—441no—
486C23×C4—441no—
487C23×C4—441no—
488C23×C4—441no—
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C2×M16—22no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—114no—
495C2×M16—222no—
496C2×M16—441no—
497C2×M16—441no—
498C2×M16—441no—
499C2×M16—441no—
500C22×C8—111no—
501C22×C8—111no—
502C22×C8—111no—
503C22×C8—111no—
504C22×C8C22×D1111yescharacteristic
505C22×C8C22×D1111yescharacteristic
506C22×C8C22×D1111yescharacteristic
507C22×C8C22×D1111yescharacteristic
508#120—224no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—441no—
512C4×D4—441no—
513C4×D4—441no—
514C4×D4—441no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4C4×D1111yescharacteristic
518C2×C22⋊C4—111no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—111no—
522C2×C22⋊C4—111no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—111no—
525C2×C22⋊C4—111no—
526C2×C22⋊C4—111no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4C4×D1111yescharacteristic
529C2×C22⋊C4C4×D1111yescharacteristic
530C2×C42—111no—
531C2×C42—111no—
532C2×C42C22×D1111yescharacteristic
533C4⋊C8—222no—
534C4⋊C8—441no—
535C4⋊C8—441no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538C22⋊C8—41no—
539C22⋊C8—222no—
540C22⋊C8—222no—
541C22⋊C8—222no—
542C22⋊C8—222no—
543C22⋊C8—222no—
544C22⋊C8—222no—
545C22⋊C8—441no—
546C22⋊C8—441no—
547C22⋊C8—441no—
548C22⋊C8—441no—
549#97—441no—
550C4×C8—222no—
551C4×C8—441no—
552#95—111no—
553#95—111no—
554#95—111no—
555#95—111no—
556#95—111no—
557#95—111no—
558C2×C11—42no—
559C2×C11—81no—
560C2×C11#232111yescharacteristic
561C2×C11#293311yescharacteristic
562C2×C11D4×M1611yescharacteristic
563C2×C11#297411yescharacteristic
564C2×C11#297511yescharacteristic
565C2×C11#297611yescharacteristic
566C2×C11#297811yescharacteristic
567D11—42no—
568D11—42no—
569C24—111no—
570C24—111no—
571C24—222no—
572C24—222no—
573C24—222no—
574C24—441no—
575C24—441no—
576C24—441no—
577C24—441no—
578C24C2×C4×D1111yescharacteristic
579C24C2×C4×D1111yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—41no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—441no—
587C2×D4—441no—
588C2×D4—441no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—441no—
621C22×C4—441no—
622C22×C4—441no—
623C22×C4—441no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4—444no—
628C22×C4—441no—
629C22×C4—441no—
630C22×C4C2×C4×D1111yescharacteristic
631C22×C4C2×C4×D1111yescharacteristic
632C22×C4C2×C4×D1111yescharacteristic
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4D4×D1112yes—
635C22×C4#434112yes—
636C22×C4C23×D1111yescharacteristic
637M16—44no—
638M16—444no—
639M16—444no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—112no—
653C2×C8—112no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C4⋊C4—22no—
665C4⋊C4—441no—
666C4⋊C4—441no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—114no—
670C22⋊C4—222no—
671C22⋊C4—222no—
672C22⋊C4—222no—
673C22⋊C4—441no—
674C22⋊C4—441no—
675C22⋊C4—441no—
676C22⋊C4—441no—
677C22⋊C4—441no—
678C22⋊C4—441no—
679C42—21no—
680C42—21no—
681C42—221no—
682C42—221no—
683C42—221no—
684C42—221no—
685C11#2203811yescharacteristic, complemented, Sylow
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—112no—
700C23—112no—
701C23—221no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23—221no—
707C23—221no—
708C23—221no—
709C23—221no—
710C23—221no—
711C23—221no—
712C23—221no—
713C23—444no—
714C23—444no—
715C23—444no—
716C23—444no—
717C23—444no—
718C23—444no—
719C23—444no—
720C23(C22⋊D11)⋊C412yes—
721C23C22×C4×D1111yescharacteristic
722D4—44no—
723D4—444no—
724D4—444no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—112no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—221no—
754C2×C4—221no—
755C2×C4—221no—
756C2×C4—221no—
757C2×C4—221no—
758C2×C4—221no—
759C2×C4—221no—
760C2×C4—221no—
761C2×C4—444no—
762C2×C4—444no—
763C2×C4—444no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4(C22⋊D11)⋊C412yes—
773C2×C4M16×D1112yes—
774C2×C4C2×D4×D1111yescharacteristic
775C2×C4C2×#434111yescharacteristic
776C2×C4#6703711yescharacteristic
777C2×C4#6703711yescharacteristic
778C2×C4#6704211yescharacteristic
779C2×C4#6704211yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—222no—
785C8—222no—
786C8—441no—
787C8—441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—222no—
806C22—222no—
807C22—222no—
808C22—4416no—
809C22—441no—
810C22—441no—
811C22—441no—
812C22—441no—
813C22—441no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22C2×(C22⋊D11)⋊C411yescharacteristic
818C22#1062307611yescharacteristic
819C22#1062307611yescharacteristic
820C22C2×M16×D1111yescharacteristic
821C22#1062327611yescharacteristic
822C22D11×#13111yescharacteristic
823C22#1062328111yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—222no—
829C4—441no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4—441no—
834C4#1062312311yescharacteristic
835C4#1062314811yescharacteristic
836C4#1062314811yescharacteristic
837C4#1062318411yescharacteristic
838C2—42no—
839C2—81no—
840C2—442no—
841C2—442no—
842C2#1307127911yescharacteristic
843C2#1307734611yescharacteristic
844C2#1307734811yescharacteristic
845C2#1307764811yescharacteristic
846C2#1307765411yescharacteristic
847C2#1307766311yescharacteristic
848C2#1307767511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#66990C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#22038
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. C2×#10622739C2semidirect
4. #13069412C2semidirect
5. #13069408C2semidirect
6. #13069230C2semidirect
7. #13069223C2semidirect
8. #13069220C2semidirect
9. #13069220C2semidirect
10. #13068911C2semidirect
11. #13068911C2semidirect
12. #13068799C2semidirect
13. #13068525C2semidirect
14. #13068402C2semidirect
15. C11×#1870C2semidirect
23. C22×#4318C22semidirect
25. C2×C11×C22⋊C8C22semidirect
26. C2×C11×C22⋊C8C22semidirect
30. C2×C22⋊(C11⋊C8)C22semidirect
40. C2×#66879C22semidirect
41. C2×Dic11⋊C8C22semidirect
42. C2×Dic11⋊C8C22semidirect
43. C2×C8×Dic11C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4×C11⋊C8C22semidirect
55. C11×#336C22semidirect
56. C11×#336C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622188C22semidirect
115. C2×#4318D4semidirect
241. (C2×D11)⋊C4M16semidirect
273. #1870D11semidirect
403. C2×C22⋊C8C2×D11semidirect
404. C2×C22⋊C8C2×D11semidirect
422. #336C2×D11semidirect
423. #336C2×D11semidirect
685. C11#22038semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106226252
C2×#106227392
C4×#669902
#130694122
#130694082
#130692302
#130692232
#130692202
#130689112
#130687992
#130685252
#130684022
C11×#18702
#2203811